Equilibrium and cooperation in repeated hierarchical games

Research outputpeer-review

Abstract

In the paper a two-level infinitely repeated hierarchical game with one player (center) C0 on the first level and S1...Sn subordinate players on the second is considered. On each stage of the game player C0 selects vector x=(x1....xn) from a given set X, in which each component represents vector of resources delivered by C0 to one of subordinate players, i.e. (formula presented). At the second level, Si i=1,2..,n, choose the controls (formula presented), where Yi(xi) depends upon the choice of player C0. In this game, a set of different Nash equilibrium also based on threat and punishment strategies is obtained. In one case, the center enforces special behavior of subordinate firms (vector of manufactured goods), threatening to deprive them of resources on the next steps if the subordinate firms refuse to implement the prescribed behavior. In another case, the subordinate firms can force the center to use a certain resource allocation threatening to stop production. Using different combinations of such behaviors on different stages of the game, we obtain a wide class of Nash equilibrium in the game under consideration. The cooperative version of the game is also considered. The conditions are derived under which the cooperative behavior can be supported by Nash Equilibrium or Strong Nash Equilibrium (Nash Equilibrium stable against deviations of coalitions).

Original languageEnglish
Title of host publicationMathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings
EditorsMichael Khachay, Panos Pardalos, Yury Kochetov
PublisherSpringer
Pages685-696
Number of pages12
ISBN (Print)9783030226282
DOIs
Publication statusPublished - 1 Jan 2019
Event18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019 - Ekaterinburg
Duration: 8 Jul 201912 Jul 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11548 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019
CountryRussian Federation
CityEkaterinburg
Period8/07/1912/07/19

Fingerprint

Nash Equilibrium
Game
Resource allocation
Cooperative Behavior
Resources
Coalitions
Resource Allocation
Deviation
Choose
Business

Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Petrosyan, L., & Pankratova, Y. (2019). Equilibrium and cooperation in repeated hierarchical games. In M. Khachay, P. Pardalos, & Y. Kochetov (Eds.), Mathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings (pp. 685-696). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11548 LNCS). Springer. https://doi.org/10.1007/978-3-030-22629-9_48
Petrosyan, Leon ; Pankratova, Yaroslavna. / Equilibrium and cooperation in repeated hierarchical games. Mathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings. editor / Michael Khachay ; Panos Pardalos ; Yury Kochetov. Springer, 2019. pp. 685-696 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Petrosyan, L & Pankratova, Y 2019, Equilibrium and cooperation in repeated hierarchical games. in M Khachay, P Pardalos & Y Kochetov (eds), Mathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11548 LNCS, Springer, pp. 685-696, Ekaterinburg, 8/07/19. https://doi.org/10.1007/978-3-030-22629-9_48

Equilibrium and cooperation in repeated hierarchical games. / Petrosyan, Leon; Pankratova, Yaroslavna.

Mathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings. ed. / Michael Khachay; Panos Pardalos; Yury Kochetov. Springer, 2019. p. 685-696 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11548 LNCS).

Research outputpeer-review

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Petrosyan L, Pankratova Y. Equilibrium and cooperation in repeated hierarchical games. In Khachay M, Pardalos P, Kochetov Y, editors, Mathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings. Springer. 2019. p. 685-696. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-22629-9_48